I found a workaround yesterday, but I can't explain why it is working.
If you delete AdGuard VPN connection in iOS settings, which will disable AG DNS, and setup NextDNS in AG application, it will work. Also, I realized after a while, that some third parties DNS have also that issue like ControlD but some not like Rethink DNS. I just can't explain why.
So if anyone is facing this issue, this is the solution while AdGuard dev solve this issue that I reported to their support.
This isn't a good response. You could say that for all others third DNS parties. Then, why offering a DNS section where you can add your own DNS provider?
AG copes with Safari cosmetic, NextDNS for the DNS and Windscribe for the VPN. Best of breed strategy.
Anyway there is a bug and the dev team is aware of it now. The bug, an old one just appeared again with AG new release.
Issue Details AdGuard version: Adguard Pro for iOS 4.2.1 Device model: iPhone XR Operating system and version: iOS 14.7.1 Expected Behavior New, custom DNS upstream is added to list of DNS servers ...